The Pricing Kernel Equation

27 Pages Posted: 8 Feb 2019

See all articles by Akira Yamazaki

Akira Yamazaki

Hosei University - Graduate School of Business Administration

Date Written: January 26, 2019


This paper provides an equation called the pricing kernel equation, which relates the subjective probability distribution on an arbitrary asset price to the risk-neutral probability distribution. It claims that the subjective probability distribution is priced by a static option portfolio, in which the weight of an option is determined by the level of the pricing kernel. As an application, we propose a new method for estimating empirical pricing kernels. Another application is to extract subjective probabilities and fundamental statistics from option prices. These examples show that the pricing kernel equation can be a versatile tool for various applications.

Keywords: subjective probability, risk-neutral probability, pricing kernel equation, reciprocal kernel, option market, static replication, absolute risk aversion

JEL Classification: G12, G17

Suggested Citation

Yamazaki, Akira, The Pricing Kernel Equation (January 26, 2019). Available at SSRN: or

Akira Yamazaki (Contact Author)

Hosei University - Graduate School of Business Administration ( email )


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